Definition:Metrizable Topology

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Let $\struct {S, d}$ be a metric space.

Let $\struct {S, \tau}$ be the topological space induced by $d$.

Then for any topological space which is homeomorphic to such a $\struct {S, \tau}$, it and its topology are defined as metrizable.

Also see

  • Results about metrizable topologies can be found here.

Linguistic Note

The UK English spelling of metrizable is metrisable, but it is rarely found.